SOME COMPLEXITY IN TOPOLOGICAL DYNAMICS
Guo Hua Zhang
School of Mathematics and Statistics University of New South Wales Sydney 2052,
Australia and School of Mathematical Sciences Fudan University Shanghai 200433, China
zhanggh@fudan.edu.cn
By a topological dynamical system we mean a compact metric space equipped with a
surjection. Given a topological dynamical system, people are interested in the study of
complexity of the system. In this talk, we shall discuss some variants of complexity of
a topological dynamical system: topological (sequence) entropy, weak mixing and Li-Yorke
chaos. The first part concerns the relationship between them for a general topological
dynamical system and then the second part concerns their relationship for one
dimensional systems.

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